Yeah my curiosity was more around what activity you were doing in calibre that meant you thought applying a search restriction was necessary rather than just working with the search results. Since working with a list often implies the desire to add more books to it - which you can't do once you have applied a restriction...
The discussion of the tag browser from theDucks has reminded me of another solution to your original request. You can configure a reading list to apply a tag or set a custom column value when a book is added to a list (and remove it when the book is taken off it). So you could do that in combination with the tag browser to see the contents of a list by clicking on your specific tag name (or custom column if configured to display in the tag browser). So while your reading list name itself won't appear in the tag browser, an appropriately named tag or similar would give the same effect.